Prediction of Individual Tree Diameter Using a Nonlinear Mixed-Effects Modeling Approach and Airborne LiDAR Data

Abstract

Rapidly advancing airborne laser scanning technology has become greatly useful to estimate tree- and stand-level variables at a large scale using high spatial resolution data. Compared with that of ground measurements, the accuracy of the inferred information of diameter at breast height (DBH) from a remotely sensed database and the models developed with traditional regression approaches (e.g., ordinary least square regression) may not be sufficient. Thus, this regression approach is no longer appropriate to develop accurate models and predict DBH from remotely sensed-related variables because DBH is subject to the random effects of forest stands. This study developed a generalized nonlinear mixed-effects DBH estimation model from remotely sensed imagery data. The light detection and ranging (LiDAR)-derived stand canopy density, crown projection area, and tree height were used as predictors in the DBH estimation model. These variables can be more readily measured over an extensive forest area with higher accuracy compared to the conventional field-based methods. The airborne LiDAR data for a total of 402 Picea crassifolia Kom trees on a sample plot that were divided into 16 sub-sample plots and located in the most important distribution region of western China were used. The leave-one sub-sample plot-out cross-validation method was applied to evaluate the model’s prediction accuracy. The results indicated that the random effects of the sub-sample plot on the prediction of DBH were large and their inclusion into the DBH model significantly improved the prediction accuracy. The prediction accuracy of the proposed model at the mean (M) response was also substantially improved relative to the accuracy obtained from the base model. Among several tree selection alternatives evaluated, a sample size of the two largest trees per sub-sample plot used in estimating the random effects showed a significantly higher accuracy compared to other sampling alternatives. This sample size would balance both the measurement cost and potential prediction errors. The nonlinear mixed-effects DBH estimation model at the M response can also be applied if obtaining the estimates of individual tree DBH with a relatively lower cost, and a lower prediction accuracy was the purpose of the study.

Individual Tree Diameter Estimation in Small-Scale Forest Inventory Using UAV Laser Scanning

“…ε ij is the error term. Due to the residual variance increasing with respect to the prediction, a power-type variance function (Equation (2)) was applied for correcting the variance heterogeneity [62,63]:…”

“…Then, the selected base model was expanded as a generalized model through the inclusion of various covariate predictors. Besides tree height, DBH is also influenced by the tree's size, competition status, and stand characteristics [24,25,63]. We assessed the influence of other LiDAR-derived parameters on DBH by a two-step covariate selection approach for the generalized DBH estimation modeling.…”

“…ε i is the within-group error, following a normal distribution with an average value vector of zero and a variance-covariance matrix R i [32]. σ 2 is the scaling factor for residual dispersion common to all sites; G i is a diagonal matrix of within-sample site heteroskedasticity variances in which diagonal elements were provided by the variance function Equation 2; Γ i is simplified as an identity matrix, considering no correlation patterns within the same sample site [63]. The NLME models were fitted to all observations using the NLME package [68] in the R environment ( www.r-project.org) by the method of restricted maximum likelihood (REML).…”

Modeling Height–Diameter Relationship for Poplar Plantations Using Combined-Optimization Multiple Hidden Layer Back Propagation Neural Network

“…Özçelik et al [17] used the single hidden layer with only one or two hidden nodes in the neural network and they did not investigate the effects of multiple hidden layers on the precision of the neural network model and determination of appropriate forms of the transfer functions. Our study is substantially different from the previous studies [13][14][15][16][17][18][19][20], because we proposed the method of selecting the optimal model through application of the "trial and error approach" [30], k-fold cross-validation approach [31] and combinatorial optimization approach. It can help determining the structure of the neural network, such as the hidden layer nodes, transfer functions and the number of hidden layers.…”

“…The parameters in the developed mixed-effects height-diameter model were estimated by maximum likelihood using the Lindstrom and Bates (LB) algorithm implemented in the R software (version 3.2.2) nlme function based on fitting dataset [27]. Detailed descriptions of the mixed-effects modeling are presented in the references [28][29][30][31].…”